Is it possible to have different background images for different visible layers?
This isn't possible by default with the Background Images subset in the Properties panel, whichever image you have set to a view is what will show across all layers.

An alternative however is to use Empties with their Display type set to Image as detailed in my answer here. This way you can just move the specific empty with the blueprint to the layer with the object you are working on. To have this not obscure or interfere with your work, just open the Outliner and restrict these from being selected (the cursor icon).

(Notice that I switch from Layer 1 to Layer 2)



A similar method to the above is to enable the Import Images as Planes addon and create two planes, one for each image. These can be placed in any layer, and display of the images can be enabled or disabled separately for each image by using the outliner window, or by careful placement of the planes in layers, and enabling or disabling the visibility of the layer.